BOOTSTRAP Subcommand (NLR command)

BOOTSTRAP provides bootstrap estimates of the parameter standard errors, confidence intervals, and correlations. BOOTSTRAP can be used only with CNLR; it cannot be used with NLR.

Bootstrapping is a way of estimating the standard error of a statistic, using repeated samples from the original data set. This process is done by sampling with replacement to get samples of the same size as the original data set.

  • The minimum specification is the subcommand keyword. Optionally, specify the number of samples to use for generating bootstrap results.
  • By default, BOOTSTRAP generates bootstrap results based on 10*p*(p+1)/2 samples, where p is the number of parameters. That is, 10 samples are drawn for each statistic (standard error or correlation) to be calculated.
  • When BOOTSTRAP is used, the nonlinear equation is estimated for each sample. The standard error of each parameter estimate is then calculated as the standard deviation of the bootstrapped estimates. Parameter values from the original data are used as starting values for each bootstrap sample. Even so, bootstrapping is computationally expensive.
  • If the OUTFILE subcommand is specified, a case is written to the output file for each bootstrap sample. The first case in the file will be the actual parameter estimates, followed by the bootstrap samples. After the first case is eliminated (using SELECT IF), other procedures (such as FREQUENCIES) can be used to examine the bootstrap distribution.

Example

MODEL PROGRAM A=.5 B=1.6.
COMPUTE PSTOP=A*SPEED**B.
CNLR STOP /BOOTSTRAP /OUTFILE=PARAM.
GET FILE=PARAM.
LIST.
COMPUTE ID=$CASENUM.
SELECT IF (ID > 1).
FREQUENCIES A B /FORMAT=NOTABLE /HISTOGRAM.
  • CNLR generates the bootstrap standard errors, confidence intervals, and parameter correlation matrix. OUTFILE saves the bootstrap estimates in the file PARAM.
  • GET retrieves the system file PARAM.
  • LIST lists the different sample estimates, along with the original estimate. NCASES in the listing (see OUTFILE Subcommand (NLR command)) refers to the number of distinct cases in the sample because cases are duplicated in each bootstrap sample.
  • FREQUENCIES generates histograms of the bootstrapped parameter estimates.